That's quote from a college level introduction to CRT. Look at the bottom of page 1.
'Woke' is slang for possessing what Marxists call "Critical Consciousness". That's always been what it means in the political sense regardless of how various people have used it.
The Critical Theory praxis involves "awakening" people to their oppression. Listen to some of the diehards...they talk about systems of oppression the way Fundies talk about Satan. And that's an apt metaphor since it's a Gnostic Cult. Max Horkheimer said that it is impossible to make a moral judgement within the current order because people's values are so off track and only when people achieve "liberation" from these systems of oppression can we see what's really true. The obvious response to that is how would he know that and the only answer is that it's a form of Gnosticism.